Population divergence, including speciation and the origins of population structure, is the fundamental evolutionary process leading to the diversity of life. This research project will extend recent advances in a likelihood-based approach to divergence models. The new approach employs analytic integration over prior distributions of model parameters within a Markov chain Monte Carlo framework. The method leads to a joint probability density function, proportional to the likelihood that can be used for parameter estimation and log- likelihood ratio tests of nested demographic models. The new method will be adapted to general multi-population problems in divergence. Such problems have long been appreciated as requiring both a population genetic perspective and a phylogenetic perspective. The research plan outlines how these two can be brought together under a common MCMC simulation. This will be the first such method that does not assume a given phylogeny;that does not assume that gene flow has not occurred;and that makes no assumptions about the relative population sizes of sampled or ancestral populations. By providing estimates of the joint posterior density, proportional to the likelihood, the method will provide direct access to log-likelihood ratio tests and to likelihood-based confidence intervals. The approach will also be extended to problems in sample identification and DNA barcoding. These new methods will be applied to a case study of divergence among species and subspecies of Chimpanzee. The methods will also be applied to large multi-population multi-locus data sets from human populations.